1) Both inner surface ends of the truncated cone must have been made out of copper. Otherwise the cavity would not have the correct boundary conditions to be a resonant cavity: it would be a waveguide. One wouldn't be able to have high Q and resonance if the inner surface of the ends wouldn't be copper.

While copper is a preferred material for waveguides. (Because it is cheaper than gold for example) It isn't the only material a resonant cavity can be made of. As a matter of fact, the inner surface of tubes I work with are regularly gold plated, while the rest of the structure is copper. Copper loves to oxidize and turn green, so much of what I see is copper, and plated with gold. We also pressurize with nitrogen and/or dry air to keep the oxidation down and not spend money on long lengths of fancy gold plated waveguide.

Also a resonant cavity is a waveguide, with both ends shorted.

Some are purpose build too, like magnetrons (collection of resonant cavities)

The point is, that you can take an ordinary waveguide, weld the ends shut and it is now a resonant cavity.

The smoother the better, to decrease scattering. Definitely no dents allowed or you get standing waves or arcing. You don't need to polish the thing. EHF frequencies need to be very very smooth. The lower frequencies, who cares.

Notice the 1.5inch dims in yellow in the foreground and background. Because of depth perception, one is behind the test article and the other is in front. That creates a situation where you can't rely on the 1.5inch reference without knowing the viewing angle of the camera and at least one length in the Z axis of the chamber...

Well, I took anudder look at your sketch, and still stick with my interpretation. The camera appears to be damn near perpendicular to the centerline of the cone, and perpendicular to the z-axis of the large end diameter which is nearly centered on the lens of the camera. If anything, the rear of the cone rim is slightly to the left of center, but I ignored that.

I note that the support is not at right angles to the plane of the large diameter of the cone, and not at all at right angles to its own vertical support Faztek, but I don't think that matters.

What matters to the camera is that the Faztek horizontal support is centered on the cone's axis. If that is the case, the dimension that I show should be spot on within a plus or minus. The support is clearly not vertically off center, but it may be nearer or further from the camera than the centerline of the cone's axis. I can't tell, and I can't help that.

The other support that you dimension appears to be a 3" chunk of Faztek, at least to this pair of retinas.

It is evident that the last entry on the table is significantly different: the ratio for Length to SmallDiameter is significantly larger than the other two, this ends up having a very large effect on ( L/SmallDiameter - L/BigDiameter): 77% higher. The first two rows on the table are closer to each other.

This is due to the ratio of the SmallDiameter to the Length. Since all three rows are closer as to the ratio L/BigDiameter, it necessarily follows that the discrepancy is due to the magnitude of the SmallDiameter.The last row on the table has a value for the SmallDiameter in proportion to the length and in proportion to the BigDiameter that differs considerably from the first two rows.

If one magnifies or reduces both x and y axis by the same ratio on both the vertical and horizontal axes, the ratio L/SmallDiameter should stay the same.

So, this would indicate that John's last numbers should be scaled down proportionally accordingly. One Faztek cross-section appears on the foreground, then the truncated cone and then on the background is the other Faztek cross-section. This should not have any effect on the values computed by McCulloch' formula based on the present values supplied by John (McCulloch' formula is only dependent on the ratios L/Diameter and therefore not on the absolute magnitude).

So, for McCulloch's formula calculation there is no need to change the magnitude of John's values.

But the magnitude is important for Frobnicat's analysis since many of the equations investigated depend on the magnitudes.

Still learning about evanescent fields. I found some good resources from the field of total internal reflection fluorescence microscopy. I see lots of data out there about evanescent fields around waveguides too. The same methodology can be applied to RF and waveguides it seems. I'm getting closer to calculating the evanescent field penetration depth of RF through copper. This is an interesting learning experience. In retrospect to my training as a young pup, it is clearer now why adjacent waveguides are kept separated from each other. I remembering learning that, but the details of why were left out.

Has anyone else looked at this Chinese theory/cavity design paper? It is interesting that the author used finite element integration of the Maxwell equations over the cavity volume to determine the most favorable modes and cavity dimensions, and to predict thrust. I bet someone on here could run the same analysis using free finite-difference time-domain (FDTD) software.

4 ConclusionMicrowave thrusters without propellant does not require propellant, so without erosion from the high temperature gas stream, erosion and heat transfer problem, the performance of the thrusters is not affected by the working environment, at the same time, increasing the spacecraft quality, using different material for the structure can increase the range of thrust, suitable for use in space and near space spacecraft.

There are two ways to explain this new thrusters,

(1) from the Planks hypothesis and Einsteins quantum theory of light, also the theory of microwave to explain the thrust from the thrusters, that is to quantise the injected microwave to the sealed cavity into photons, its travelling speed is the group speed, photons and the thrust cavity wall elastic collision produce the net thrust,

(2) From the classic theory of electrodynamics to explain how the thrust is produce by the thrusters, according to the kinetic energy and conservation of momentum of the electromagnetic system within its volume, Maxwell equation and electromagnetic flux density vector can found out the source of the thrust is coming from the integration of the electromagnetic tensor along the surface of the volume.

Using finite element numerical method to numerical analyse the classical Maxwell equation of electric field of the idealised conical resonator, to obtain the model and practical of the distribution of the electric field of the cavity under 1000W. By analyse the properties under different modes and the different properties. Calculation show that under the four modes, TE011, TE012, TE111 and TM011, the quality factor of TE012 is highest and with highest thrust, followed by TE011. With the Small End of the cavity unchanged, the quality factor and thrust decrease with the increase in the Large End.

The TE10 mode rectangular waveguide is suitable for use in modes TE011 and TE012, and coupling to the side wall of the resonator in where the magnetic field is relatively strong, coupling using coaxial cable is suitable in modes TE011 and TM011, in axis of the resonator where electric field is relatively large.With 1000W microwave input, using brass as the material of the cavity, using the classical theory of electrodynamics, the maximum theoretical thrust produced in modes TE011 and TE012 is 411mN and 456mN respectively, and the practical measurements are 214mN and 315mN.

Of course this does not explain conservation of momentum of a spacecraft using these thrusters, only the force distributions within the resonate cavity.

This sentence stands out -

Quote

With the Small End of the cavity unchanged, the quality factor and thrust decrease with the increase in the Large End.

I believe the author is referring to "increase in the large end" relative to the ideal geometry derived near the start of the paper.

Thank you so much for bringing up this information. There is a lot of useful information here. In this post, I would like to emphasize the following:

Quote

By analyse the properties under different modes and the different properties. Calculation show that under the four modes, TE011, TE012, TE111 and TM011, the quality factor of TE012 is highest and with highest thrust, followed by TE011. With the Small End of the cavity unchanged, the quality factor and thrust decrease with the increase in the Large End.

The TE10 mode rectangular waveguide is suitable for use in modes TE011 and TE012, and coupling to the side wall of the resonator in where the magnetic field is relatively strong, coupling using coaxial cable is suitable in modes TE011 and TM011, in axis of the resonator where electric field is relatively large.With 1000W microwave input, using brass as the material of the cavity, using the classical theory of electrodynamics, the maximum theoretical thrust produced in modes TE011 and TE012 is 411mN and 456mN respectively, and the practical measurements are 214mN and 315mN.

We now have separate confirmation in both China and the USA that thrust force measurements are related to the TRANSVERSE ELECTRIC modes, since their mode shape result in greater thrust force/PowerInput than the TRANSVERSE MAGNETIC mode shapes.

This is a further challenge [ and a hint ] to explaining the measured thrust forces in these EM Drives as resulting from the magnetic field interacting with the Earth's magnetic field or with other magnetic fields (like the magnetic damper)

It also explains why NASA Eagleworks explored resonance for the mode TE012

EDIT: Electric and magnetic fields are two interrelated aspects of the same electromagnetic tensor; the split of this tensor into electric and magnetic fields depends on the relative velocity of the observer and charge. Therefore my original wording (challenge to thought process) should be changed to "challenge and hint". It is a powerful hint to make us think as to what is going on.

The interaction with the Earth's magnetic field is challenged because of experimental data changing the orientation of the drive. Shawyer had the EM Drive also positioned vertically and also positioned horizontally, and also rotating continuously around a vertical axis. If there is a magnetic interaction with the Earth's field it is a challenge to explain the same thrust force and intrinsic direction with the EM Drive positioned vertically and horizontally and with the NASA Eagleworks to flip the drive in the horizontal direction as well. (think of the right hand rule)

This is a further challenge to explaining the measured thrust forces in these EM Drives as resulting from the magnetic field interacting with the Earth's magnetic field or with other magnetic fields (like the magnetic damper)

That is a Quantum Leap Doc......Except for the fact that the magnetic field lines are oscillating about the Z axis (small end to big end). The direction we're thrusting.

A study of any issue is moot without the observer possessing a healthy dose of skepticism, and sufficient training in knowing the difference between logic and logical fallacy, and not falling prey to cognitive bias.

With the Small End of the cavity unchanged, the quality factor and thrust decrease with the increase in the Large End.

I don't know Chinese, so I cannot read the original paper, but I notice that the translator writes that the cavity was made of brass. I wonder whether this is a translation issue where the translator substituted "brass" for what should have been copper (or another copper alloy other than common brass).

My interpretation of what the translator actually wrote above is that keeping the diameter of the small base of the truncated cone constant, that Q and the thrust force decrease as one increases the diameter of the large base. I know this contrary to McCulloch's formula and contrary to expectations, but this is what the translator wrote.

We now have separate confirmation in both China and the USA that thrust force measurements are related to the TRANSVERSE ELECTRIC modes, since their mode shape result in greater thrust force/PowerInput than the TRANSVERSE MAGNETIC mode shapes.

This is a further challenge to explaining the measured thrust forces in these EM Drives as resulting from the magnetic field interacting with the Earth's magnetic field or with other magnetic fields (like the magnetic damper)

It also explains why NASA Eagleworks explored resonance for the mode TE012

It almost seems that the Magnetic field is interacting with Space itself in this case, much how gravity distorts spacethis configuration of a magnetic field appeasrs to be doing the same thing.

1) If one computes the net forces produced by the magnetic field and by the electric field (which are standing waves) the net forces sum up to zero. It is a closed system. There is no net thrust on the center of mass using Maxwell's equation.

2) I have to read the Chinese papers again, but my recollection is that they use Minkowski's stress tensor instead of Abraham's stress tensor. Minkowski's stress tensor is asymmetric. Mass cannot be asymmetric (there must be a center of mass ! ), that's why Abraham imposed symmetry of the tensor from the outset. When using Mynkowski's stress tensor one has to consider an open system together with hidden momentum (as done by Shockley). If the Chinese got a net force without considering any non-classical physics effect, it seems to me that they must not have adequately considered hidden momentum. In other words, using Minkowski's stress tensor cannot be by itself an explanation of thrust.

3) The Chinese translator's statement <<With the Small End of the cavity unchanged, the quality factor and thrust decrease with the increase in the Large End.>> poses further questions regarding their analysis.

4) The experimental fact that the Transverse Electric field modes result in greater Q and greater force measurements than the Transverse Magnetic modes is valuable and stands on its own (apart from their analysis of force).

]There cannot be any significant irregularities on the inside surface of the truncated cone.

I don't know if the inside has been polished, and neither do you. The outside has only a mill finish, somewhat tarnished by handling. The thickness of the various plates and what have you might be 1/8" in thickness.

Your words were, that there cannot be "significant" irregularities on the inside surface of the cone. If the inside is finished like the outside, then I don't think that the loose term which you used, and which I accept for purposes of discussion, is "sufficiently" regular.

Since you did not specify the level of polishing, nor the "flatness" of the conical section line, nor the surface qualities of the copper, yours is but a suggestion.

Quote from: Rodal

No, it was not a suggestion. It is not based on words, or intuition. It follows from Maxwell's equations.

I took a guess that the level of polishing on Hubble's mirrors would be sufficient. Somewhere between mill finish and Hubble polish, there is a "sufficiently" regular finish.

Obviously Hubble is not optimized for M/W reflectance, and I merely mention a reflective analogy because of the importance of establishing a lossless reflection of the M/W's in the cavity.

Savvy?

Quote from: Rodal

John, you just cannot have a high Q with a poor, irregular surface on the inside, when the skin depth is a couple of micrometers or less. You don't need to exaggerate...

John, if there is no inner copper on the ends of the cavity (showing PCB board on the outside) then you cannot have a resonant cavity, so the inner surface ends must have been made out of highly-conductive material like copper.

Oh, I get that. Show me the copper, however. I'm assuming it's there too. I make no objections, but ask about the quality of the mirrored finish on the inside of the device; an inside which no forum human has witnessed.

As to 1.5" & 3" Faztek. If my assumption that the horizontal member, which I took to be 1.5" or 3.81 cm is NOT in the center of the device, then my A1.4 measurement is way off.

Looking again at the piece of Faztek jutting out towards the camera, and looking at the catalog, I see a straightforward resemblance to the 3" square Faztek, not the 1.5" Faztek.

We now have separate confirmation in both China and the USA that thrust force measurements are related to the TRANSVERSE ELECTRIC modes, since their mode shape result in greater thrust force/PowerInput than the TRANSVERSE MAGNETIC mode shapes.

This is a further challenge to explaining the measured thrust forces in these EM Drives as resulting from the magnetic field interacting with the Earth's magnetic field or with other magnetic fields (like the magnetic damper)

It also explains why NASA Eagleworks explored resonance for the mode TE012

It almost seems that the Magnetic field is interacting with Space itself in this case, much how gravity distorts spacethis configuration of a magnetic field appeasrs to be doing the same thing.

This is my thinking:

It is the electric field modes (not the magnetic modes) that show the greater Q and greater thrust, not the other way around. There is no such thing as "thrust" using classical Maxwell's equations. It is a closed system. The magnetic field vectors from both bases point towards the center. There is no net magnetic force on the center of mass using classical Maxwell's equations.

If on the other hand, one uses non-classical physics it doesn't follow that the force must come from the magnetic field, on the contrary, for example McCulloch's explanation of inertial changes due to Unruh radiation, it is the photons inertia that matters.

As to polishing, all that is required is to use a Profilometer on the surface and be smooth enough to less than a fraction of a micrometer because the skin depth is ~2 micrometers. That does not need to be a mirror surface. Not Hubble mirror. Not mirror on the wall. No nanometer profile.

Is this the 3" by 3" Faztek that you referring to?

(If not could you please post the specific 3" by 3" Faztek picture you are referring to?)

Because that looks very different from this 1.5" by 1.5", which looks much more as to what is in Brady's

Me a primitivo-man without AutoCAD and just looking at picture and just counting

Me a pre-AutoCad-man just looking at 2 slots per side on the 3"by3" and 1 slot per side on the 1.5" by 1.5"

Well, alrighty then. Look at my A1.2 PDF. The Faztek image there is real blurry on account of the TIFF having been enlarged by 50 some odd times. So, mea culpa on that. Didn't occur to me to go back to the original JPEG.

Now. Is the horizontal piece that I use as 1.5" (3.81cm) in the center of the device? If so, then my extrapolation should be correct to plus or minus. If not, and the horizontal member is further to the rear, then again, my extrapolation is bogus.

Me needum drinkum. Will see mixologistum tomorrowum.

Edit:

Loooked harder. I don't think that the 1.5" Faztek thingy is in the center of the copper can. I think it is behind the whole assembly. Not at all sure I go with Mulletron's guess as to the dimensions of the can. All I can say is that the proportions, but not the dimensions I sketched out, are reasonably accurate.

I note that we are spending a lotta time arguing about these dimensions. The good Doctor asked, rather politely a hundred or more pages ago, but got only partial dimensional answers. Since then Paul March decided to go mum. Easily answered questions go without answer, which reflects on those who experiment, not on those who try to understand.

Of the two end pieces seen in the photo, the upper one is a different extrusion from the lower one, and does not project closer to the camera than the lower one.

Same paper as before except the original Chinese language version, but this time I went to the end. There exists an abstract in English of another related paper after the reference section. It says "Copper" is used.

Quote

Abstract：Aim．The introduction of the full paper reviews Refs．1 and 2 and points out that we find that the methodof Ref．2，authored by Qiu Xiaoming et al and originally used on a completely different research project，is very effectivefor performing our performance calculations，which we explain in sections l。2 and 3．Section l briefs Ref．1，whose billy author，Roger Shawyer，proposed a theory of microwave propulsion of spacecraft．Sections 2 and 3explain how we apply Ref．28 method；their core consists of：(1)wi凼t}le finite element method。we simulate theMaxwell8 field equations for the microwave radiation thruster in the roundtable cavity；(2)we acquire the resonantmodes of the round-table cavity and the electromagnetic fields of 1000W inside the roundtable cavity；(3)weanalyze the characteristics of the microwave radiation thruster of different cavity s叽ctures and at different resonantmodes；(4)the simulation results，presented in Tables 1 and 2，and their analysis show preliminarily that：(1)the quality factor and thrust at TE012 mode are the largest；(2)for the incident microwave of 1000W and 2．45GHz，with copper as the thrusterB material．the largest theoretical thrust based on the classical theory of electrodynamicsis 41 1 and 456mN respectively at TEoll and TEol2 modes．

Of course this introduces another mistake. We are sure that the frequency was not 45 GHz. No, it is spacing, caused me to misread "and 2 . 45 GHz". It is intended to read as "and 2.45 GHz", which is right.

Same paper as before except the original Chinese language version, but this time I went to the end. There exists an abstract in English of another related paper after the reference section. It says "Copper" is used.

Quote

Abstract：Aim．The introduction of the full paper reviews Refs．1 and 2 and points out that we find that the methodof Ref．2，authored by Qiu Xiaoming et al and originally used on a completely different research project，is very effectivefor performing our performance calculations，which we explain in sections l。2 and 3．Section l briefs Ref．1，whose billy author，Roger Shawyer，proposed a theory of microwave propulsion of spacecraft．Sections 2 and 3explain how we apply Ref．2’8 method；their core consists of：(1)wi凼t}le finite element method。we simulate theMaxwell’8 field equations for the microwave radiation thruster in the round—table cavity；(2)we acquire the resonantmodes of the round-table cavity and the electromagnetic fields of 1000W inside the round—table cavity；(3)weanalyze the characteristics of the microwave radiation thruster of different cavity s叽ctures and at different resonantmodes；(4)the simulation results，presented in Tables 1 and 2，and their analysis show preliminarily that：(1)the quality factor and thrust at TE012 mode are the largest；(2)for the incident microwave of 1000W and 2．45GHz，with copper as the thruster’B material．the largest theoretical thrust based on the classical theory of electrodynamicsis 41 1 and 456mN respectively at TEoll and TEol2 modes．

Congratulations on another excellent find. I posted it at McCulloch's giving you credit.

QUESTION: Have you found any pictures? Any dimensions on the Chinese EM Drive?

How can it be postulated that Evanescent Waves by themselves can solve the closed-system, momentum-conservation problem?

They can't by themselves using classical physics. One spaceship may transmit an evanescent field to move external small nanosatellites next to it (would not be an interesting form of propulsion, and the center of mass composed by the nanosatellites and the spacecraft system would not accelerate either). But it cannot move itself just by using Evanescent waves without any external field.

A spaceship cannot propel itself by using Evanescent Waves any better than it can propel itself using Electromagnetic Fields. It is a closed system.

A swimmer can swim in the ocean because the ocean water has its own inertia and resists acceleration. An astronaut cannot propel itself by waving her arms and legs in space.

To enable propulsion one must have an open system: external dark matter, external fields: like the Earth's magnetic field, an external aether, even consideration of the external quantum vacuum, etc. But certainly not just Evanescent Fields by themselves that are self generated and only interacting in a closed system.

To avoid this confusion one must rely on conservation principles: conservation of momentum, conservation of energy, and variational principles.